Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3×C31 |
| direct product | A4×#15668333 |
| Fitting, socle, derived, Hall | C22×C312 ⋊ C32 |
| Sylow | C312 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×#15668333 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C312 | C32 |
| LCS | G ▷ C22×C312 | |
| UCS | C1 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 372 |
1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 169);